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Teramoto, Yoshiaki; Tomoeda, Kyoko

Optimal Korn’s inequality for solenoidal vector fields on a periodic slab. (English) Zbl 1263.35012

Proc. Japan Acad., Ser. A 88, No. 10, 168-172 (2012).
Summary: We obtain the best constant in Korn’s inequality for solenoidal vector fields on a periodic slab which vanish on a part of its boundary. To do this we consider the Stokes equations with Dirichlet boundary conditions, following H. Ito [Math. Methods Appl. Sci. 17, No. 7, 525–549 (1994; Zbl 0801.73014); Japan J. Ind. Appl. Math. 16, No. 1, 101–121 (1999; doi:10.1007/BF03167526)].

Cited in 2 Documents

MSC:

35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
35B45 A priori estimates in context of PDEs

Keywords:

best constant; Stokes equations; Dirichlet boundary conditions

Citations:

Zbl 0801.73014
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Full Text: DOI Euclid

References:

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[7] H. Ito, Optimal Korn’s inequalities for divergence-free vector fields with application to incompressible linear elastodynamics, Japan J. Indust. Appl. Math. 16 (1999), no. 1, 101-121. · Zbl 1306.74008 · doi:10.1007/BF03167526
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